Thermodynamic basis for a variational model for crystal growth

Variational models provide an alternative approach to standard sharp interf ace models for calculating the motion of phase boundaries during solidifica tion. We present a correspondence between objective functions used in varia tional simulations and specific thermodynamic functions. We demonstrate tha t variational models with the proposed identification of variables are cons istent with nonequilibrium thermodynamics. Variational models are derived f or solidification of a pure material and then generalized to obtain a model for solidification of a binary alloy. Conservation laws for internal energ y and chemical species and the law of local entropy production are expresse d in integral form and used to develop variational principles in which a '' free energy," which includes an interfacial contribution, is shown to be a decreasing function of time. This free energy takes on its minimum value ov er any short time interval, subject to the laws of conservation of internal energy and chemical species. A variational simulation based on this model is described, and shown for small time intervals to provide the Gibbs-Thoms on boundary condition at the solid-liquid interface. [S1063-651X(99)02307-7 ].